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AP Calculus AB 2002 Free Response Questions - Complete Paper (pdf)

- Let f and g be the functions given by f(x) = e
^{x}and g(x) = ln x.

(a) Find the area of the region enclosed by the graphs of f and g between x = 1/2 and x = 1.

(b) Find the volume of the solid generated when the region enclosed by the graphs of f and g between x = 1/2 and x = 1 is revolved about the line y = 4.

(c) Let h be the function given by h(x) = f(x) - g(x). Find the absolute minimum value of h(x) on the closed interval 1/2 ≤ x ≤ 1, and find the absolute maximum value of h(x) on the closed interval 1/2 ≤ x ≤ 1.

Show the analysis that leads to your answers. - The rate at which people enter an amusement park on a given day is modeled by the function E defined by
- An object moves along the x-axis with initial position x(0) = 2. The velocity of the object at time t ≥ 0 is given by v(t) = sin(&pi/3 t).
- The graph of the function f shown above consists of two line segments. Let g be the function given by
- A container has the shape of an open right circular cone, as shown in the figure above. The height of the container is 10 cm and the diameter of the opening is 10 cm. Water in the container is evaporating so that its depth h is changing at the constant rate of -3/10 cm/hr.
- Let f be a function that is differentiable for all real numbers. The table above gives the values of f and its derivative f' for selected points x in the closed interval -1.5 ≤ c ≤ 1.5. The second derivative of f has the property that f''(c) > 0 for -1.5 ≤ c ≤ 1.5.

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